Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2012, Article ID 563864, 35 pages
doi:10.1155/2012/563864
Research Article
Automatic Human Gait Imitation and
Recognition in 3D from Monocular Video with
an Uncalibrated Camera
Tao Yu1, 2 and Jian-Hua Zou1, 2
1
Systems Engineering Institute, School of Electronic & Information Engineering,
Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
2
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an,
Shaanxi 710049, China
Correspondence should be addressed to Tao Yu, yvt9399@stu.xjtu.edu.cn
Received 26 September 2011; Accepted 16 December 2011
Academic Editor: Yun-Gang Liu
Copyright q 2012 T. Yu and J.-H. Zou. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
A framework of imitating real human gait in 3D from monocular video of an uncalibrated
camera directly and automatically is proposed. It firstly combines polygon-approximation with
deformable template-matching, using knowledge of human anatomy to achieve the characteristics
including static and dynamic parameters of real human gait. Then, these characteristics are
processed in regularization and normalization. Finally, they are imposed on a 3D human motion
model with prior constrains and universal gait knowledge to realize imitating human gait. In
recognition based on this human gait imitation, firstly, the dimensionality of time-sequences
corresponding to motion curves is reduced by NPE. Then, we use the essential features acquired
from human gait imitation as input and integrate HCRF with SVM as a whole classifier, realizing
identification recognition on human gait. In associated experiment, this imitation framework is
robust for the object’s clothes and backpacks to a certain extent. It does not need any manual assist
and any camera model information. And it is fitting for straight indoors and the viewing angle for
target is between 60◦ and 120◦ . In recognition testing, this kind of integrated classifier HCRF/SVM
has comparatively higher recognition rate than the sole HCRF, SVM and typical baseline method.
1. Introduction
Recently, the investigation on human gait is receiving more and more attention. Especially, in
monitoring, human gait is the only one characteristic that can be recognized in long distance
without contacting. Hence, the study on it lies at an important status in safeguard area.
In medicine, human gait study is valuable in relative diagnosis and modifying bones for
patients.
2
Mathematical Problems in Engineering
As an important branch of human gait study, human gait imitation does not only help
to investigate deeply in real motion—it can acquire the valuable cue of sight characteristic
that is hard to get from the raw images directly, making the results more clear. e.g., some
characteristics on human body cannot be detected continually because of the sheltering or by
themselves as human is motioning. By the means of imitating human gait, we can adjust the
relative motion model at any viewing angle, any time to detect and analyze—but also owns
broad scope of application in virtual reality and 3D TV.
At present, most studies on imitating motion use multicamera to realize reconstruction
of motion in 3D 1–5. These methods share obvious style: solving the problem of sheltering
directly in object’s motion, and the results are remarkable for various poses of human motion
at the expense of complex camera model information and complex computations.
Also, there are many attempts to restore human motion in 3D or to track human
motion from monocular video sequence directly. However, most do not only need training
to learn and estimate poses but also need manual help originally. For example, 6 needs to
initialize the 2D parameter values for the first frame manually by overlaying a model onto
the 2D image of the first frame. Reference 7 sets initialization by matching the first frame to
six key poses acquired by manual clustering, and the pose having minimal matching error is
chosen as the initial pose. Reference 8 involves some prior information which was extracted
from some hand-labeled data. In 9, the local model needs information of contour extracted
manually from real images.
Some need the information of relative camera, such as 10 which recovers 3D model
of humans from just one frame or a monocular video sequence using a simplification of
the camera model based on a collinearity condition. In 11, the webcam used needs being
calibrated at the phase of preprocessing. Reference 12 needs both to estimate camera
information and to locate joints manually in the first frame of video sequences.
Some have other too many demands or constraints. For example, 13 subjects to not
only Gaussian prior and Gaussian stabilizers but also the objective time-consuming based on
its covariance-scaled sampling. Reference 14 needs to detect pedestrian’s motion trajectory
and footprints throughout the segmented video sequence by associated clustering technique.
15, 16 need both relative information of edges and textured regions. And 17 needs to
preextract state subspace from one sequence of motion capture data for each motion type.
We can see that most motion imitations, whether using multicamera or using single
camera, based on numerous continuous characteristics at the cost of expensive accurate
instruments or accurate camera model information or manual assist or other extra demands.
Are these demands necessary?
For these doubts above, this paper presents a framework. It firstly combines polygonapproximation with deformable template-matching, using knowledge of human anatomy
to achieve the characteristics including static and dynamic parameters of real human gait.
Then, these characteristics are processed in regularization and normalization. Finally, they
are imposed on 3D human model with prior constrains and universal gait knowledge to
imitate real human gait, thus realizing the reconstruction of 3D human gait from monocular
video directly and automatically. The method is robust for detecting subject’s clothes and
backpack to a certain extent at 60◦ ∼120◦ angle of view in stable straight walking in test of
CAISIA gait database. Moreover, it does not need any manual assist and any camera model
information. In application of this framework, with the dimensionality of time sequences
corresponding to curves of human gait imitation reduced by the method of neighborhood
preserving embedding NPE, a kind of classifier which integrates HCRF hidden conditional
random field with SVM supported vector machine using the essential time sequence
Mathematical Problems in Engineering
3
acquired from the human gait imitation as input to realize human identification recognition
on gait and presents a higher recognition rate than using HCRF or SVM as classifier alone
and the typical baseline method in associated experiment as it contains more structural traits
of the data to be classified in space and time during dealing with them.
The remainder of this paper is arranged as follows. Section 2 interprets the basic idea
and principle of the framework on gait imitation; Section 3 describes the realization of the
method in detail; Section 4 gives the application of human gait imitation in identification
recognition; Section 5 provides relative experiment and results analysis; Section 6 concludes
this paper.
2. Principle
We all know that when people begin to know something, they used to compare the new thing
with some general mode. Then, they will carve the mode in detail by the use of characteristics
of the real thing, that is, to say, imposing individuation to the mode. Thus, a complete
impression on the new thing is formed in their minds, finally.
Here, analogously, during the course of knowing human gait, we have a prior general
human motion model firstly. Secondly, we acquire the individual characteristics of some
real gait in some way. Then, for the characteristics detected, we update the partial prior
values of the relative part in the human model; for the characteristics undetected, we use
the prior configuration of the relative part in the human model to compensate in proportion.
Thus, integrating the real individual characteristics with prior general information, we form
a sufficient and complete expression on the impression of human gait.
This idea of acquiring characteristics heuristically overcomes the phenomenon of
sheltering in human motion. It maintains the continuity of motion detection to some extent
and has strong adaptation to the situation of some characteristics hard to detect.
The basic principle for the method of gait imitation above can be described in
mathematics as both the posterior probability function P m, wm | c in formula 2.1 and
entropy function HX in formula 2.2. Here, P m is the prior knowledge of the human
model m ∈ Rm corresponding to some person, P wm | m is the prior knowledge
on gait wm ∈ Rw, likelihood function P c | wm, m is the individual characteristic
information c ∈ Rc on gait and random variable X whose range is a group of state
sequence on gait {x1 , x2 , . . . , xm } representing gait imitation:
Pt m, wm | c pc | m, wmpwm | mpm
pc | m, wmpm, wm
,
i
i
pc
i
i
i
i p c | m , wm p wm | m pm 2.1
HX m 1
Pt log
P
t
t1
where: X ∈ {x1 , x2 , . . . , xm }.
2.2
In formula 2.1, according to Bayesian rules, at time of t, basing on a certain prior
information note here the prior information is general or universal for most persons on
P m and P wm | m, the more remarkable the individual characteristic information P c |
wm, m on gait is, the bigger the value of posterior probability function P m, wm | c will
be. Then, at this time, in formula 2.2, according to information theory 18, 19, the value of
4
Mathematical Problems in Engineering
The universal prior knowledge
Drawing human model
Let the human model walking
(1 ) building human motion model
Detecting
and tracking
real person
Templatematching
Matching
successful?
Yes Features
pick-up
No
Video Yes
over?
Regularization
and
normalization
Mapping static and
dynamic parameters
to update relative
parts in human
motion model; for
undetected features,
using prior
configuration to
compensate
in proportion.
Application
No
(2 ) acquiring the individual characteristics
from real human gait
( 3 ) integrating real individual characteristics
with prior human motion model
Figure 1: Framework of out approach.
the relative entropy function HX will be smaller, showing that the next state closed to the
real will be more ensured. At other times, similar analysis is as above. Thus, as a result, the
whole imitation will more approximate a real person’s gait.
3. Designing
Before designing, we assume that the human gait to be detected is walking in a straight
line with a constant speed. According to the idea of Section 2, the designing includes
three parts mainly, which is displayed in Figure 1. In the first part—building the human
motion model, the universal prior knowledge for drawing human model and letting the
human model walking is equivalent to P m and P wm | m, respectively. The result of
second part—acquiring the individual characteristics from real human gait—is equivalent
to P c | wm, m. Both the former two parts based on the knowledge of human anatomy,
dynamics and kinematics. Besides, the second part uses mainly a method that combines
polygon- approximation and deformable template-matching to track and detect motional
object. The third part that integrates real individual characteristics with prior human motion
model is equivalent to the principle of formula 2.1 and 2.2, which is realized mainly on
updating partial both static and dynamic parameters as well as relative compensations.
3.1. Building Human Model in Prior Knowledge
3.1.1. Drawing for the Whole Human Model
Referring to the standard of H-Anim 20 in VRML virtual reality modeling language 21,
the human model of this paper is illustrated in Figure 2. Figure 3 gives the relative 3D human
model. The general structure of the 3D human model in this paper, with the crotch of the
human model in the center of the world coordinates, consists of three parts: trunk, upper
limbs, and lower limbs. As can be seen, except for head, hands, and feet, the basic cell is
that a sphere plus a cylinder side by just as Figure 4. The cylinder denotes bone, and the
sphere denotes joint of bones in the human model. The three parts above are connected
with such cells in different direction. In detail, in each joint of the human model, we build
a local coordinate to make its z-axis in the same direction of the axis of the next bone. All
Mathematical Problems in Engineering
5
+Y
Head
Neck
Breast
Shoulder
The
upper
arm
Belly
Elbow
Waist
Forearm
Abdomen
Hip
Wrist
Crotch
+X
Hand
Thigh
Knee
Crus
Ankle
Foot
Figure 2: 2D human model.
the parts above begin from the origin of the world coordinates. Firstly, we configure the pose
of the local coordinates. Then, we draw a cell in the local coordinates. Next, we move the
local coordinates to the end of the cell. Again, we configure the pose of the local coordinates
and draw the next cell. Thus, we take that turn repeating until all the parts are drawn over
finally. That is shown in Figure 5, where N equals the total number of the cells in each
part above. Trotate x , Trotate y , and Trotate z stand for the rotating matrixes in x, y, and z axes,
respectively. Ttranslate x , Ttranslate y , Ttranslate z stand for the translating matrixes in x, y, and z
axes, respectively.
Consequently, combining Figure 2 with Figure 3 again, the designing for trunk begins
from crotch up, consisting of 6 segments: head, neck, chest, belly, waist, and abdomen. The
designing for upper limbs begins from neck down, consisting of 4 segments: shoulders, the
upper arms, forearms, and hands. Here, from crotch to neck, we do not draw any cell, but
configure the pose of the local coordinates and move the local coordinates because we have
drawn the trunk at first. The designing for lower limbs begins from crotch down, consisting
of 4 segments: hip, thigh, calf, and feet. The last cell of each part above should be replaced
with relative part of head, hand, and foot. That is sphere or cuboid. Thus, the human model
has 22 segments overall, each of which has 3 degrees of freedom DOFs. Plus additional
6
Mathematical Problems in Engineering
Figure 3: 3D human model.
Figure 4: Basic cell in model structure.
3 DOFs for global rotation, so there are 22 × 3 3 69 DOFs for the whole human model.
Because hands and feet themselves affect human pose little in motion, by simplification, the
overall number of DOFs is 69 − 4 × 3 57.
When the human model above is in motion, the display of motion for the model is
realized on adjusting poses of the cells in the model and updating the display continuously
when we draw the cells.
3.1.2. The Universal Prior Knowledge for the Human Motion Model
According to the knowledge of human anatomy 22–24, combining with the H-Anim
standard, if we assume the model’s height is H, then: head occupies 0.13H; shoulders’ width
is 0.26H; the width of the hip is 0.19H; when the upper limbs are horizontal, the width
between left and right hand equals H; the midpoints of the lower limbs correspond to the
knees of the model; the lengths of the upper arm, forearm, and hand are 0.19H, 0.15H, and
0.11H, respectively.
When the model is in walking mode, according to the knowledge of human dynamics
and kinematics 25–30, as Figure 6 displaying, a normal walking mode can be described as
follows.
The upper limbs swing backwards and forwards on the left and right sides in turn.
At one time, so do the lower limbs. The phrases of the motion for the upper limbs and the
lower limbs are in contrary. That is, when the upper limbs swing forward on the left side, the
lower limbs swing forward on the right side, and when the upper limbs swing forward on the
right side, the lower limbs swing forward on the left side, thus to and fro. During walking,
Mathematical Problems in Engineering
7
Begin from origin
(x = 0; y = 0; z = 0)
Initialization: i = 0
Configure direction of pose
× Trotate x (i) × Trotate y (i) × Trotate z (i)
Draw cell
(i)
Move local coordinates to the end of the cell
× Ttranslate x (i) × Ttranslate y (i) × Ttranslate z (i)
Configure direction of pose
× Trotate x (i + 1) × Trotate y (i + 1) × Trotate z (i + 1)
Draw cell
(i + 1)
N
i=i+1
Draw over?
(i + 1 = N − 1?)
Y
Current part
draw over
Figure 5: Flow chart for designing every part of the human model.
the neck is slightly bending forward. And especially, the elbows and knees are both in cycles
of slight bending and stretching. Simultaneously, the shoulders and hips, corresponding to
relative limbs, are also swinging slightly back and forth. With the limbs in motion, the trunk,
including head are also swinging wiggly, turning clockwise and anticlockwise, slightly. In
addition, there are some constrains: the elbows can bend forward only; the knees can bend
backward only, the extent of bending in the elbow increases to maximum when the relative
part of upper limbs swings to front end and decreases to minimum when the relative part
of upper limbs swings back end; the extent of bending in the knee decreases to minimum
when the relative part of lower limbs swings to front end and increases to maximum when
the relative part of lower limbs swings back end.
The prior parameters above on structure and motion in model will be updated
partially after the actual parameters of some real individual are acquired.
3.2. Acquiring the Individual Characteristics from Motional Object in Reality
3.2.1. Detecting and Tracking Motional Object
This paper processes the video images of real human gait using graying, background modeling and updating, background subtracting, binary conversion, and binary morphological
8
Mathematical Problems in Engineering
a
b
c
d
e
f
g
h
i
j
Figure 6: A normal walking mode for the human model.
operation in turn to acquire the actual motional object firstly. Secondly, consulting 31, we
use a method of connectivity to retrieve all the contours and reconstruct the full hierarchy
of nested contours of motional object. Then, we compress horizontal, vertical, and diagonal
segments, leaving only their ending points. Thus, we acquire the external contour of the
actual motional object. Finally, referring to 32, the polygon curve is approximated with
assigned accuracy. When the overall number of vertexes of the polygon is 4, we begin to
carry on a deformable template matching to acquire the individual characteristics of the real
human gait. The principle of deformable template-matching is as in Figure 7.
3.2.2. The Principle of Deformable Template-Matching
In Figure 7, the points a, b, c, and d correspond to the vertex of head, crotch, left ankle and
right ankle, respectively. Assume that their coordinates are Xa, Y a, Xb, Y b, Xc, Y c, and
Xd, Y d, respectively. So the constraining rules are
Y a > Y b > Y c, Y d,
Xc < Xb < Xd.
3.1
Mathematical Problems in Engineering
9
a
θ
e
α
b
Y
c
O
d
X
Figure 7: Principle of deformable template-matching.
We can infer that only when the space between lower limbs of the object is the biggest
or so, the deformable template-matching can be in effect. In other words, at the moment, the
matching is successful probably.
According to the knowledge of human anatomy 22–24, in Figure 7, if we assume the
length from the crotch to the top of head in human is h, the neck is about 0.75 h away from
the crotch, and the waist is 0.30 h away from the crotch or so. Then, we connect the waist
with left ankle and right ankle respectively, so the middle position of the connected parts can
be known as knees. Thus, we confirm the motion position of the lower limbs approximately
at the moment. Because of the variety of the upper limbs’ motion, moreover, some parts of
the upper limbs have little effect on gait, the estimation of the structure and motion for the
upper limbs is achieved by proportion to the prior human motion model completely. Thus, all
the signs above on human object’s body are marked automatically, not requiring any manual
work, once the deformable template-matching is successful.
Figure 8 shows the actual form of deformable template-matching. Because the prior
model sets the crotch and hip in the same horizontal line by simplification and in motion, the
model itself has been added with the slight bend of elbows, knees and neck in proportion as
universal prior knowledge before imitating real human gait in 3D, consequently, the errors
that the measured lengths for limbs are probably shorter than the real lengths because of the
bends of real joints can be compensated to a certain extent. This strategy saves processing
time effectively.
3.2.3. Regularization and Normalization for Detected Characteristics
Because there is some information on depth-variance for the motion of detected object, to
the same part in reality, the lengths detected at the different time, different position differ in
values possibly. Hence, in order to be uniform approximately, the lengths detected need to
10
Mathematical Problems in Engineering
Figure 8: Actual form of deformable template-matching.
b
c′
b′
c
a
a′
Figure 9: Principle of regularization.
be regularized and normalized. The principle of regularization in this paper is illustrated in
Figure 9:
√
√
c
cc
c
c
c
c
c c
c
×
×
√
.
√
√
√
a
b
a
b
ab
ab
a b
a b
3.2
In Figure 9, the two rectangles are alike in shape and different in size. We assume
that this phenomenon results from the same object being detected in different distances or
depths from view. The line segments c and c differ in direct measurement, but according
to the analysis of formula 3.2, as long as we divide them by the square root of area of
the relative smallest circumscribable rectangle or other circumscribable shapes, the two
different measurements in directivity will be transformed into equivalent forms, that is, the
changed forms can act as the expressions of real size. Figure 10 shows the form of actual
deformable template-matching with circumscribable rectangle for real motional object.
This paper regularizes the lengths of every part of detected object in the light of
the principle above. Then, we divide the accumulated regularized lengths of each part in
the whole sample process by respective sample count to achieve the mean value of each
part. Next, we divide the mean values by the height of the object to acquire the proportions
Mathematical Problems in Engineering
11
Figure 10: Form of the actual deformable template-matching with rectangle inside for real motional object.
of all the parts, realizing the normalization. In addition, in Figure 7, the step is measured
based on the maximum angle α between two thighs; so for this variable, we do not need
any regularization and normalization, but use law of cosines and the relative inverse
trigonometric function to achieve its value when the space between two thighs is maximum.
As for the obliquity θ of trunk, it is measured with inverse tangent function computed
by the differences of x-coordinates and y-coordinates each between the hip and the top of
head, furthermore, acquiring its mean. The actual obliquity θ of trunk may lean forward or
backward, which is decided by the sign of result. The corresponding formula is in 3.3, where
l equals length of relative part; X and Y stand for x-coordinate and y-coordinates of relative
position; Nsample is sample amount; Arectangle is the area of the smallest circumscribable
rectangle for object. Finally, all the parameters above are regarded as the final results of real
detected individual characteristics:
Nsample lmean i
ltemp / Arectangle
Nsample
i
,
lmean
,
lae mean lec mean led mean /2
2
2
2
− lcd
lec led
,
α max arccos
2 × lec × led
lproportion Nsample θ
i
3.3
arctgXb − Xa /Ya − Yb i
.
Nsample
3.2.4. Transforming from General Viewing Angle to Silhouette
In theory, any angle of view can be decomposed into two parts in horizontal and vertical
directions, that is, any viewing angle can be regarded as the synthesizing from the two kinds
12
Mathematical Problems in Engineering
γl
γv
Y
A
O
X
H
Figure 11: The decomposing principle of a general viewing angel for a common camera.
γl
A
a
γl
Moving direction
θ
a
′
e
γl
θ
γl
′
b
′
e
Y
c
γl
O
B
α
h
α′
b
d
′
X
X′
c′
h′
d′
Watching
Figure 12: The projection of the deformable template in horizontal obliquity direction.
of viewing angles. Figure 11 gives the decomposing principle of a general viewing angel
for a common camera, where γl and γv are the obliquities of the camera against the flat A
in horizontal and vertical directions. Basing on these parameters, Figures 12 and 13 display
the projections of the deformable template mentioned in horizontal and vertical directions,
where the blue figure is the real gait detecting in flat A, the red figure is the watching result
in flat B, and the green lines are relative assistant lines. In Figures 12 and 13, according to the
relationships of the coordinates between the projection in flat A and the original graph in flat
Mathematical Problems in Engineering
13
γv
a γv
γv
a′
Moving direction
γv
e′
α
γv
θ
θ′
Watching
γv
e
′
α
b′
b
′
h
Y′
c′
Y
d′
c
h
B
d
A
O
X
Figure 13: The projection of the deformable template in vertical obliquity direction.
B, the transforming computation and distance computation of coordinates to a general angle
of view can be inferred as formula 3.4:
xin flat A lMN in flat A xat viewing angle r
,
cosrl yin flat A 2
yat viewing angle r
,
cosrv 2
3.4
xM in flat A − xN in flat A yM in flat A − yN in flat A .
In this paper, the angle of view is defined as that the facing direction of detected object
circles anticlockwise from walking direction to watching screen, forming the angle. Namely,
rl 90 − rviewing angle ,
rv 0.
3.5
From formula 3.5 above, it can be found that when the viewing angle rviewing angle
is about 90 degree or so, the associated cosine function approximates 1 in formula 3.4. So,
at this time, in formula 3.4, the viewing angle can be ignored for the relative transforming
computation at a certain extent.
And in reality, strictly speaking, the viewing angle for a real camera is changing
because of the limited range of eyesight by the camera itself even if the camera fixes position,
just as Figure 14.
In Figure 14, at the fixed leaning angle r for a real camera, when the motion object the
red rectangle is moving from position A to B and C, we can see that the relative viewing
angle is changing and the relative transforming computation should base on the associated
viewing angle at special some position according to formula 3.4. Especially, when the object
is moving to the position B, the relative viewing angle is 90 degree. At this moment, according
14
Mathematical Problems in Engineering
Motion object
n
A
io
t
ec
r
g
o
n
vi
M
di
rA
B
rB
C
rC
r
O
Watching
Figure 14: The real viewing angle changes with the motion object at fixed camera.
to the analysis above, the angle can be ignored during the transforming computation. This
paper, in subsequent experiment, we will find that the detecting deformable templatematching is often successful at this angle or so because the triangle template can be in effect
only when the both shoulders of subject, nearly in overlapping or in approximate verticality
over viewing. And considering the normalization and average in formula 3.3, thus, the
viewing angle can be omitted during transforming computation to a great extent.
3.3. Integrating Real Individual Characteristics of Detected Motional Object
with Prior Human Motion Model
The process that this paper maps for both the parameters of structural proportion and motion
for the real motional object above onto the 3D human model is as follows.
3.3.1. Mapping Static Parameters
This paper configures the height of human model used for gait imitation in some constant
prior value. Then, integrating with the proportions of all the parts on trunk and lower limbs
in Section 3.2, we figure out the relative lengths. For lengths of all the parts of the upper limbs,
we default the normal prior values of the human model.
3.3.2. Mapping Dynamic Parameters
This paper substitutes the maximum angle α between two thighs and the obliquity θ of trunk
detected in reality both for relative prior values. When the limbs of the human model in walk
are swinging backward and forward, the condition of switching between left side and right
side is based on step, so, the span of the upper limbs swinging to and fro is in proportion to
the step of the lower limbs.
Mathematical Problems in Engineering
15
Figure 15: Final form of motion imitation.
3.4. Interpretation and Relative Analysis for the Final Motional Form of the
Mapped Human Model
Figure 15 shows the final form of motion for the mapped human model and draws the curves
of motion for the model’s main joints including ankles, knees, hips, wrists, elbows, shoulders
and the top of head in real time. According to analysis, the asymmetry exists in the curves
because there are cycles of slight bow in elbows and knees when the limbs swing backward
and forward on both sides. Besides, the curves of the upper limbs in reality need the curves
in the lower limbs to synthesize. Note that in Figure 15, the size of video image for detecting
motional object is 320 × 240, and the size of image for imitating motion is 362 × 522 initially.
Here, because of the limitation in page size, we decrease sizes of the images by unchanging
proportion between width and height of image. And we set angles of view for the human
motion model and the real motional object to be same for the convenience of observation in
contrast similar intention for the subsequent same kinds of images. In fact, we can transform
the viewing angle of the human motion model freely to observe after it achieves the actual
individual characteristics on motion and updates by itself.
In order to study deeply, we draw the relative curves accurately in MATLAB tool
by using the data corresponding to the real-time curves acquired from the development
environment of VC6.0 in Figure 15. This is shown in Figure 16. Next, we combine Figure 15
with Figure 16 to understand the characteristics of the curves from important parts in the
motional model.
For ankles, when the corresponding lower limb rises from the last position of body
and the knee bends backward, the highest position of the ankle’s curve is reached. Then,
this lower limb begins to swing forward, and the curve begins to decline. After the limb’s
motion passes the trunk, the curve begins to rise. When the limb swings to front end, because
the knee can only bend backward and can not bend forward furthermore, at one time, the
extent of the bending is the smallest compared with the whole motion process, the curve rises
to the higher position. Then, the limb begins to fall to the ground. Because the horizontal
displacement from front end to the ground is quite short, the curve begins to decline with
higher slope than before. As the landing of the limb is finished, the curve declines to the
lowest position. Next, it is turn of the part in opposite side of body to motion in the same
style, thus, time after time. In respect of wrists, similarly, the differences from ankles’ motion
exist in that the elbows can only bend forward and cannot bend backward. So, when part of
16
Mathematical Problems in Engineering
6
Head motion
4
Shoulder motion
Y (position)
2
Elbow motion
Wrist motion
0
Hip motion
−2
−4
Knee motion
−6
Ankle motion
−8
−2
X(
−1
po
0
siti
on
)
1
2
20
0
−20
−40
−60
Z (time)
−80
−100
−120
Right side
Left side
Figure 16: Curves of human gait imitation.
the upper limbs swings to front end, the relative wrist’ curve arrives at the highest position,
and when the upper limb swings to back end, the curve arrives at the higher position. While
the upper limb’s motion passes by the trunk, the curve arrives at the lowest position. Notice
that in reality, although the curves of the upper limbs need the curves in the lower limbs
to synthesize, both curves change with the same trend generally in horizontal and vertical
directions. Therefore, they affect each other with the same tendency. Specifically, when the
upper limbs swing to front end and back end, corresponding to the highest position, and the
higher position, the lower limbs swing also to front end and back end. Moreover, at one time,
for the lower limbs, the part of front end does not bend and the part of back end does not
rise yet, as a result, the body’s barycenter tends to rise. While the upper limbs swing parallel
with the trunk, the lower limbs swing parallel with the trunk too and slightly bend in order
to exchange the phase of the swinging. So, the body’s barycenter tends to decline.
For knees, during the swinging of lower limbs, in fact, the motional displacement from
last position to front end for one lower limb is approximately two times that from front end to
last position for another lower limb compared with ground; therefore, in motion, the length
of curve of swinging forward is bigger than that of swinging backward for knees, which
conforms to reality basically. As for elbows, similarly, furthermore, the tendencies of changes
are the same in both curves of upper limbs and lower limbs’ relative parts from description
above, so the length of elbow’s curve of swinging forward is also bigger than that of swinging
backward in motion, which consists with reality too.
For shoulders, when relative part of the upper limbs swings forward, with trunk’s
twist, the corresponding shoulder produces a short offset forward and upward and when
the relative part swings backward, with trunk’s reverse twist, the shoulder produces a short
offset backward and downward. To hip, also, its motion style is just as shoulders except that
the phases are opposite with shoulders on the same side and the extents of motion are smaller
than shoulders.
Mathematical Problems in Engineering
17
For head, during the process of swinging in both sides of the upper limbs, because of
both the inertia of arms dragging the trunk and twisting motion existed in trunk itself, head
swings slightly leftward and rightward, always towards the part of upper limbs swinging
backward.
The above analysis is mainly based on the characteristics of human anatomy. According to the analysis, the curves on imitating motion are basically consistent with the actual
characteristics of human gait. In terms of the results of subsequent experiment, different individuals differ mainly in the values of parameters of these curves, but general shapes of the
curves do not change essentially.
4. Application to Identification Recognition on Gait
As an application, we will utilize the features of curves acquired from the framework of
human gait imitation proposed in this paper, combining with associated classifier, to realize
human identification recognition. Figure 17 displays the principle of this gait recognition.
Here, firstly, because of the periodicity for human gait, only one gait cycle is used to study
by letting the human model walk for two steps. Then, all the curves are arrayed in sequences
respectively. Thus, each curve of human gait imitation can be regarded as a time sequence.
Next, the problem of recognition is transformed into the problem of dealing with all the data
of time sequences.
4.1. NPE for Reducing the Dimensionality of Time-Sequences
In reality, the lengths of the time-sequences are very long and perceptually meaningful
structure of the sequences is of much lower dimensionality, so dimensionality reduction is
needed. Considering that all the time-sequences of the curves are correlated with each other
for the same person, and these correlations are important individual characteristics, so, these
structural correlations should be preserved as much as possible while carrying on reducing
dimensionality.
Referring to 33, the method of neighborhood preserving embedding NPE aims
at preserving the local neighborhood structure on the data manifold and is less sensitive
to outlier than principal component analysis PCA. Comparing to the recently proposed
manifold learning algorithms such as Isomap and locally linear embedding, NPE is defined
everywhere, rather than only on the training data points. So, we adopt this method to reduce
dimensionality:
2
x
−
W
x
min ij j i
i j
with constraints:
XI − WT I − WX T a λXX T a
Wij 1, j 1, 2, . . . , k,
4.1
j
where X x1 , . . . , xk , I diag1, . . . , 1,
yi AT xi a0 , a1 , . . . , am−1 T xi
where yi is a m-dimensional vector.
4.2
4.3
The method in detail is just as 33, whose main principle is displayed in formulas
4.1–4.3. Before applying 33, note, here, each time-sequence i i 1, . . . , 13 × 3 39
produced by associated curve is regarded as data point xi . To preserve the property of
18
Mathematical Problems in Engineering
Walk in 3D
X01
X01
X13
X13
X02
X12
X03
Real
Infer person
or walks
in Imitate
train 2D
X11
X10
X05
X04
Walk two steps
X11
X08
X03
X10
X05
X09
X06
X08
X07
X07
List each curve
in sequence
Database
Gait database
Number of X person
X
SVM
train/infer
X01A
X01B
X01C
X02A
X02B
X02C
X03A
X03B
X03C
X04A
X04B
X04C
X05A
X05B
X05C
X06A
X06B
X06C
X07A
X07B
X07C
X08A
X08B
X08C
X09A
X09B
X09C
X10A
X10B
X10C
X11A
X11B
X11C
X12A
X12B
X12C
X13A
X13B
X13C
HCRF
Time sequence
train/infer
X04
Get one gait cycle
X06
X09
X02
X12
1A (t1-1 ,..., t1-m )
1B (t1-1 ,..., t1-m )
1C (t1-1 ,..., t1-m )
2A (t2-1 ,..., t2-m )
2B (t2-1 ,..., t2-m )
2C (t2-1 ,..., t2-m )
3A (t3-1 ,..., t3-m )
3B (t3-1 ,..., t3-m )
3C (t3-1 ,..., t3-m )
4A (t4-1 ,..., t4-m )
4B (t4-1 ,..., t4-m )
4C (t4-1 ,..., t4-m )
5A (t5-1 ,..., t5-m )
5B (t5-1 ,..., t5-m )
5C (t5-1 ,..., t5-m )
6A (t6-1 ,..., t6-m )
6B (t6-1 ,..., t6-m )
6C (t6-1 ,..., t6-m )
7A (t7-1 ,..., t7-m )
7B (t7-1 ,..., t7-m )
7C (t7-1 ,..., t7-m )
8A (t8-1 ,..., t8-m )
8B (t8-1 ,..., t8-m )
8C (t8-1 ,..., t8-m )
9A (t9-1 ,..., t9-m )
9B (t9-1 ,..., t9-m )
9C (t9-1 ,..., t9-m )
10A (t10-1 ,..., t10-m )
10B (t10-1 ,..., t10-m )
10C (t10-1 ,..., t10-m )
11A (t11-1 ,..., t11-m )
11B (t11-1 ,..., t11-m )
11C (t11-1 ,..., t11-m )
12A (t12-1 ,..., t12-m )
12B (t12-1 ,..., t12-m )
12C (t12-1 ,..., t12-m )
13A (t13-1 ,..., t13-m )
13B (t13-1 ,..., t13-m )
13C (t13-1 ,..., t13-m )
NPE
Time sequence
dimension
reduction
(m<<n)
Change each curve
dimensions
from 3D to 1D
1A (x1-1 ,..., x1-n )
1B (y1-1 ,..., y1-n )
1C (z1-1 ,..., z1-n )
2A (x2-1 ,..., x2-n )
2B (y2-1 ,..., y2-n )
2C (z2-1 ,..., z2-n )
3A (x3-1 ,..., x3-n )
3B (y3-1 ,..., y3-n )
3C (z3-1 ,..., z3-n )
4A (x4-1 ,..., x4-n )
4B (y4-1 ,..., y4-n )
4C (z4-1 ,..., z4-n )
5A (x5-1 ,..., x5-n )
5B (y5-1 ,..., y5-n )
5C (z5-1 ,..., z5-n )
6A (x6-1 ,..., x6-n )
6B (y6-1 ,..., y6-n )
6C (z6-1 ,..., z6-n )
7A (x7-1 ,..., x7-n )
7B (y7-1 ,..., y7-n )
7C (z7-1 ,..., z7-n )
8A (x8-1 ,..., x8-n )
8B (y8-1 ,..., y8-n )
8C (z8-1 ,..., z8-n )
9A (x9-1 ,..., x9-n )
9B (y9-1 ,..., y9-n )
9C (z9-1 ,..., z9-n )
10A (x10-1 ,..., x10-n )
10B (y10-1 ,..., y10-n )
10C (z10-1 ,..., z10-n )
11A (x11-1 ,..., x11-n )
11B (y11-1 ,..., y11-n )
11C (z11-1 ,..., z11-n )
12A (x12-1 ,..., x12-n )
12B (y12-1 ,..., y12-n )
12C (z12-1 ,..., z12-n )
13A (x13-1 ,..., x13-n )
13B (y13-1 ,..., y13-n )
13C (z13-1 ,..., z13-n )
Figure 17: The principle of integrated classifier for gait recognition based on gait imitation.
correlation among curves, the way to construct adjacency graph is KNN, and K is set 39. That
is to say, each time-sequence is reconstructed by adjacent other 38 time-sequences in motion
model. And it is reasonable to assume that each local neighborhood is linear although these
data points might reside on a nonlinear submanifold. Then, we use formula 4.1 to compute
the weight matrix W of the structural relation existed in the data points, use formula 4.2 to
compute the projections on reducing dimensionality and use formula 4.3 to realize the final
transformation of reducing dimensionality for each data point xi , in turn.
Originally, each of the motional curves in the human model for one gait cycle has 90
3D space samples. By using NPE, the corresponding time-sequences’ dimensionality reduces
from 90 dimension of one gait cycle to 39 dimension and the local manifold structure is
preserved in low-dimensional space with an optimal embedding.
4.2. Classifier Integrates SVM with HCRF for Classifying All
the Time-Sequences
During the key phase of recognition, we integrate the hidden conditional random field
HCRF with supported vector machine SVM to construct classifier. This kind of classifier
owns both merits of HCRF and SVM. On one hand, for each time-sequence, a set of latent
variables conditioned on local features can be learned, while the observations need not be
independent and may overlap in space and time 34. On the other hand, the separating
margins of final decision boundaries on classification are maximized in the high-dimensional
Mathematical Problems in Engineering
19
space called feature space 35. That is, it can resolve the problem of classification for the
whole multisequence existed in the same course of time.
4.2.1. HCRF for Marking All the Time-Sequences
In Figure 17, number of X X 1, 2, . . . person, according to that different joints in human
motion model corresponds to different motion curves, hence, all the curves on his motion
model, further, all the corresponding time-sequences are marked with X01A, X01B, X01C,
X02A, X02B, X02C, . . ., X13A, X13B, X13C differently, respectively.
Since all the time-sequences are correlated with each other, these observations are not
conditional independence of course. Referring to 34, 36, hidden conditional random field
HCRF which uses intermediate hidden variables to model latent structure of input domain
and defines a joint distribution over class label and hidden state labels conditioned on the
observations, with dependencies between the hidden variables expressed by an undirected
graph, does not need observations to be independent and may overlap in space and time.
And it can also model sequences where the underlying graphical model captures temporal
dependencies across frames and incorporate long range dependencies. So, using HCRF to
mark these sequences is a reasonable mode for describing them. And the mapping between
the sequences and the corresponding labels is conducted by HCRF’s training or inferring.
Here, the HCRF method which is just as 37 in principle is similar with 36. The associated
formulas are as 4.4 and 4.5:
∗
∗
P y, h | x, θ , w a ,
arg max P y | x, θ , w arg max
y∈Y
y∈Y
arg max
y∈Y
h
∗
eΨy,h,x;θ ,w
Ψy ,h,x;θ∗ ,w
y ∈Y,h∈H m e
h
n
ϕ x, j, w · θh∗ hj
where : Ψ y, h, x; θ∗ , w j1
n
θy∗ y, hj θe∗ y, hj , hk ,
j1
θ∗ arg max Lθ arg max
θ
θ
n
j,k∈E
1
log P yi | xi , θ, w − 2 θ2 .
2σ
i1
4.4
4.5
Formula 4.4 describes the principle of inferring label y from HCRF model given the
observation x, the HCRF model’s parameters θ∗ and the window parameter w which is
used to incorporate long-range dependencies. And h {h1 , h2 , . . . , hm } is a vector of latent
variables, which are not observed on training examples and where each hj is a member of
a finite set H of possible hidden states in the HCRF model. Intuitively, each hj corresponds
to a hidden state of xj with some member of H, which may correspond to “component”
structure in an observation. Ψy, h, x, θ∗ , w is a potential function parameterized by θ∗
and w. The graph E is a chain where each node corresponds to a hidden state variable at
time t; φx, j, w is a vector that can include any feature of the observation x for a specific
20
Mathematical Problems in Engineering
window size w. The inner product φx, j, w · θh ∗ hj measures the compatibility between the
observation x and hidden state hj at window size w. Each parameter θy∗ y, hj measures the
compatibility between hidden state hj and a label y. Each parameter θe∗ y, hj , hk measures
the compatibility between an edge with states hj and hk and the label y.
Formula 4.5 describes the estimation for HCRF model’s parameters θ∗ . The first term
is the logarithmic likelihood of the trained data. The second term is the log of a Gaussian prior
with variance σ 2 , that is, P θ ∼ expθ2 /2σ 2 . Combing with 37, the typical method of
conjugate gradient in 38 is used to estimate the parameters θ∗ .
In this paper, the number of hidden states is set 10 and the window size w is set
at 0,1,2 in turn to test; there are too many time-sequences in kinds and numbers to fit for
the one-versus-all HCRF model or the muti-class HCRF model directly, so the compromise
between one-versus-all HCRF model and muti-class HCRF model is adopted. In training,
each type of articular time-sequence for all the persons and its corresponding labels are
learned with a separate HCRF model. In inferring, the tested sequence is run with the HCRF
model producing the same type of articular time-sequence. The class label with the biggest
probability corresponds to the label of the test sequence.
4.2.2. SVM for Classifying All the Signs of Multisequence
In Figure 17, since from HCRF’s training, a group of labels and their corresponding motion
curves, namely, corresponding time-sequences of a specific human model are learned and
these labels’ definitions or values differ from person to person, thus, these labels can be
regarded as a group of features for a specific person. However, as there are some similarities
existed in most people’s walking styles, it is possible that from HCRF’s inferring, sometimes,
a few of these features among some persons are identical although HCRF can overcome
the overlapping of space and time to a certain extent. At this time, part of these features
is overlapping. Referring to 35, according to SVM’s property that the decision boundaries
are determined directly by the training data, as a result, the separating margins of decision
boundaries are maximized in high-dimensional space called feature space. Thus, most
nonseparable data in low-dimensional space becomes separable possibly in high-dimensional
space by mapping. So, here, SVM is used as final classifying means to recognize person by
using the marked features associated with his motion imitation as input.
Here, it is the problem of multiclass classification. On multiclass SVM, there are many
methods at present. According to relative comparison 39, the “one-against-one” approach
40, 41 is suitable for practical use. So, we use this method, which is just as 42. According
to this method, if the amount of training persons in database is K, KK − 1/2 binary
SVM classifiers are needed. Combing with 42, each classifier adopts C-support vector
classification CSVC model with RBF kernel, in which two parameters are considered: C
and γ. The two parameters are selected by using typical cross validation via parallel grid
search, and all the KK − 1/2 decision functions share the same C, γ finally.
For training data from the ith and the jth classes, formula 4.6 displays the binary
classification problem to be solved. In 4.6, the training data xi is mapped into a higher
space by the function Φ and C is penalty parameter, ζ is relaxation parameter. Minimizing
T
wij wij /2 means to maximize 2/wij , the margin between the ith and the jth classes
of data. When data are not linear separable, the penalty term C t ζij t manages to
T
balance between the regularization term wij wij /2 and reducing the number of training
errors. In addition, during final classifying, voting strategy suggested in 40, in which if
Mathematical Problems in Engineering
21
T
signwij Φxt bij infers x is in the ith class, then the vote for the ith class is added by
one, otherwise, the jth class is increased by one, is used to predict x is in the class with the
largest vote. For the case that two classes have identical vote, the one with smaller index is
selected:
min
wij ,bij ,ζij
subject to
1 ij T ij
ij
ij
where ζt ≥ 0,
ζ
w
w C
t
2
t
T
ij
wij φxt bij ≥ 1 − ζt , if xt in the ith class,
wij
T
ij
φxt bij ≤ −1 ζt ,
4.6
if xt in the jth class.
5. Performance Evaluation
5.1. Evaluation Setup and Dataset
In order to prove the ability of the application in general environment for the method
proposed in this paper, all the experiments are conducted in the environment of Microsoft
visual c6.0 at the platform of Pentium 1.73 GHz personal computer.
We test the framework proposed by this paper with the videos of CASIA gait database
43. There are 3 subsets in this database: dataset A, dataset B, and dataset C. Dataset A
viz.: NLPR consists of 20 subjects. Each subject has 12 walking sequences, which include
3 walking directions that make an angle of 0◦ , 45◦ , 90◦ , resp., with image plate and in
each direction, there are 4 walking sequences. The length of each image sequence varies from
person to person in speed.The sum of frames in each sequence is between 37 and 127. Dataset
B is a large scale of database with multiangle of view. The subset includes 124 subjects, each
of whom has 11 angles of view covering: 0◦ , 18◦ , 36◦ , 54◦ , 72◦ , 90◦ , 108◦ , 126◦ , 144◦ , 162◦ , and
180◦ and walks in 3 conditions involving: thin coat, thick coat, and backpack. Dataset C
is a large scale of database screened with infrared photography in night, in which there are
153 subjects walking in 4 conditions involving: common walk, quick walk, slow walk, and
backpack walk.
5.2. Experimental Procedures
5.2.1. For Gait Imitation
This paper uses the original videos in CASIA gait database viz. Dataset B to test the
proposed framework on gait imitation. We experiment with all the 124 subjects who walk in
thin coat, thick coat, and backpack, respectively, under different angles of view in the dataset.
Euclidean
DDI,J
sqrt
6
in − jn
2
,
5.1
n1
Mahalanobis
DDI,J
sqrt I − JT ∗ co v−1 I, J ∗ I − J .
5.2
22
Mathematical Problems in Engineering
In experiment, the whole different extent of detected parameters among the different
working conditions for the same person at the same angle of view is measured from two kinds
of distance measure: the Euclidean distance in formula 5.1 and the Mahalanobis distance
in formula 5.2, where I, J are any two groups of different detected data above and i, j are
elements in the I, J, respectively. Finally, all the results of the testing subjects are drawn in 3D
space with MATLAB R2009b tool to analyze.
5.2.2. For Gait Recognition Based on Motion Imitation
In the experiment of the application on gait imitation, we use the original videos of dataset B
in CASIA gait database to test the recognition framework which is just as Figure 17 based on
the integrated HCRF/SVM classifier at different window size w.
We adopt the leave-one-out cross validation to train/infer gait identification. In detail,
for each person, we take 5 out 6 videos with thin coat, take 1 out 2 videos with thick coat,
and take 1 in 2 videos with backpack for training. And we take the remainder one video in
thin coat, thick coat and backpack for recognizing or inferring. Next, we change the order
and repeat the train/infer experiment above until all the videos have chances of inferring. At
last, we compute the average value of these recognition rates and regard it as the final result.
The associated computation is as formula 5.3, where function inference can be regarded as
the whole function corresponding to the relative recognizing system of HCRF/SVM when
the ith subject is testing object xi xi > 0. And only when the function’s result equals input
xi , the result is correct at this time:
Rrecognition rate N
1
& xi − function inferhcrf/svm
xi ,
i
N i1
where & is the unit pulse function and & m 1 if m 0, zero otherwise.
5.3
Combing with Section 4, in training for HCRF, the method of conjugate gradient
as 38 is used to estimate associated parameters and in training for SVM, the method of
cross-validation via parallel grid search as 42 is used to estimate associated parameters.
According to Section 4, since there are 124 subjects and each subject corresponds to 13
3D time-sequences, there are 13 × 3 39 HCRF models and 124 × 124 − 1/2 7626
SVM classifiers altogether. When the training for all the subjects in the dataset B of CASIA
gait database is finished, all the trained parameters for associated HCRF models and SVM
classifiers are saved as another database.
In the area of gait recognition, baseline algorithm in 44 is a kind of typical
method which estimates silhouettes by background subtraction and performs recognition
by temporal correlation of silhouettes. So, we will compare this method with the framework
presented in this paper at recognition property. Here, during realizing 44, the silhouettes
including the actual motional object are acquired from the CASIA gait dataset B videos by
the detecting phase mentioned in Section 3. Because of the various viewing angles in the
gait database, the associated gait period is detected by computing the ratio of the number of
pixels in the silhouettes to the relative smallest circumscribable rectangle. And the leave-oneout cross validation is also adopted with the average recognition rates computed as the final
identification rates.
Mathematical Problems in Engineering
23
In addition, at the phases of just after acquiring the normalized parameters of real
detected object and just after reducing the dimensionality of associated time-sequences, we
use these temporal associated data as input with HCRF, SVM used as classifier solely to
recognize human gait. At this situation, one HCRF model corresponds to one subject, namely,
there are 124 HCRF models, and the amount of SVM classifiers is as before. Of course,
another database on associated trained parameters is produced from dataset B of CAISIA
gait database after training. At last, we conduct the comparisons of the recognition rates with
the results of recognition framework proposed by this paper at same window parameter w.
5.3. Experimental Results and Associated Analysis
5.3.1. For Gait Imitation
Figure 18 displays motion imitation for a same subject who wears thin coat, thick coat and
backpack, respectively, at angle of view of 54◦ . Observing from relative emulational model
and motion curves, the three impressions are quite similar with each other. The parameters
on real motion characteristics of the three types of walking in Figure 18 list in Table 1. The
relative measuring results of the two kinds of distances: Euclidean distance and Mahalanobis
distance are shown in Table 2. By comparing and analyzing, all the values in Table 2 are very
small universally. Namely, the whole different extent between the congener values in Table 1
is very small universally. Thus, we can infer that the detected parameters’ values listed in
Table 1 are quite close to each other.
That is to say, for the same person at the three different walking conditions, the
detected proportions, key poses of limbs, trunk in human body are almost unchanged, which
is the essential reason why the three types of walking motion imitation are alike.
Figure 19 shows the experiment of 3D gait imitation for some subjects at other angles
of view with three types of walking. By observation, comparison and relative measurement
as above, the effect of these motion imitations each quite resembles the form of relative real
individual objects in motion.
If we take columns of Table 2 as points in 3D space of Euclidean distance and the
Mahalanobis distance, respectively, we can draw a point in each of the two spaces, which
corresponds to a subject’s measurement for different extent in different walking conditions.
Similarly, Figure 20 displays the testing results of 124 subjects’ measurement on different
extent of different walking conditions at viewing angle of 54◦ , 72◦ , 90◦ , 108◦ , and 126◦ ,
respectively, in the CAISIA database. From Figure 20, we can see that most points in the two
3D spaces near origin. Whether in Euclidean or Mahalanobis measurement, the distances
between thin coat and backpack for same subject are universally slightly bigger comparing
with the other distances and because the Mahalanobis measurement includes extracovariance
matrix comparing with Euclidean measurement, the former is slightly bigger than the latter,
but they all are in acceptable ranges from the whole result. So, according to inferring as before,
it means that for each of the 124 subjects, the whole different extent of walking at different
walking conditions is comparatively small universally.
Thus, we find that the method proposed by this paper is robust in clothes and
backpack for the motional persons to a certain extent. Notice, here, the robust means that
the forms of gait imitation for the same object walking in different conditions are consistent
with each other to a great extent. Thereby, some latent constant essential characteristics for
gait are shown to some extent.
24
Mathematical Problems in Engineering
a
b
c
Figure 18: Motion imitation at three types of walking in 54◦ angle of view for the same subject a in thin
coat, b in thick coat, and c in backpack.
With regard to the experiment at other angles of view, because it is very hard for the
shape of contour of detected object to be uniform with the deformable template proposed by
this paper, or in other words, the errors are too big, the effect of relative gait imitation is failed
in those situations.
The final quality of the results for the framework of human motion imitation proposed
in this paper based mainly on analysis for the relative characteristics of human anatomy
and curves of gait, besides, the observation, comparison and associated measurement in the
experiment of CASIA gait database. It can be seen that the extent of similarity between motion
imitation and real motional object is rather large. As the motion imitation of this paper uses
Mathematical Problems in Engineering
25
Table 1: Parameters on motion imitation of three types of walking for same object.
Object
Three types of walking
Measurement
Proportion parameters to
whole stature
Angle radian
In thin coat
In thick coat
In backpack
Calvaria to neck
Neck to hip
Hip to knee
Knee to ankle
−1
1.814569 × 10
3.224494 × 10−1
2.491963 × 10−1
2.468975 × 10−1
−1
1.820641 × 10
3.229364 × 10−1
2.488364 × 10−1
2.461631 × 10−1
1.832075 × 10−1
3.206368 × 10−1
2.495140 × 10−1
2.466417 × 10−1
Step crossing angel
Trunk bend angle
4.278397 × 10−1
3.107436 × 10−2
4.233917 × 10−1
2.483856 × 10−2
4.247243 × 10−1
2.570835 × 10−2
Table 2: The whole different extent of parameters on motion imitation at three types of walking for same
object.
Whole different extent in measurement
Comparison in different types of walking
Between in thin coat and thick coat
Between in thick coat and backpack
Between in thin coat and backpack
Euclidean distance
Mahalanobis distance
7.742374 × 10−3
3.133021 × 10−3
6.709422 × 10−3
4.588733 × 10−3
1.392382 × 10−1
2.663143 × 10−1
the detected data directly come from preceding detected real object and does not execute any
prediction on poses of motion, the motion imitation is not carried out simultaneously. Here,
synchronization is not our main object. In this paper, after collecting enough information of
real person’s gait, we attempt to reconstruct human gait in 3D for other studies.
Up to now, it can be seen that the method of the deformable template-matching in
this paper not only can apply in many angles of view and is robust in clothes, backpack
for the motional persons to a certain extent, but also not need any manual work and any
model information. And it does not need fitting the motion model in each video frame
unless the outer template-matching at the key states is successful in some frames and it does
not need considering bending at elbows, knees, and neck during fitting, but compensates
in proportion as universal prior knowledge before imitating real gait in 3D finally, which
improves detecting efficiency greatly. In comparison, 7, 8 study motion imitation in 2D and
not only need manual assistant originally, but also mainly aim at silhouettes with 90◦ angle
of view and need fitting relative motion model in each frame, which is a very limited range
of angle and objective time-consuming.
5.3.2. For Gait Recognition Based on Motion Imitation
Table 3 gives the results of associated comparisons of the integrated HCRF/SVM classifiers
based on recognition application of gait imitation at different window size w and different
viewing angle with typical baseline method. Figure 21 gives the bar graph associated with
data in Table 3.
From Figure 21, combing with Table 3, we can see that the recognition rate differs
from different window size w and when w equals 1, the recognition rates are universally
higher than at other window sizes. At every tested w, when the viewing angle near 90◦ ,
including 108◦ , the recognition rates are universally higher than at other viewing angles
26
Mathematical Problems in Engineering
(a)
(a)
(b)
(b)
(c)
(A)
(c)
(B)
(a)
(a)
(b)
(b)
(c)
(C)
(c)
(D)
◦
Figure 19: Form of motion imitation in other angles of view. A 72 angle of view; B 90◦ angle of view,
C 108◦ angle of view; D 126◦ angle of view a in thin coat, b in thick coat, and c in backpack.
because the relative detected parameters including proportions of trunk and lower limbs are
more accurate than at other viewing angles. Although any viewing angle can be mapped into
90 degree viewing angle according to the transform computation mentioned, the little error
still cannot be escaped. We can also see that, at same window size w and same viewing angle,
usually the recognition rate in thin coat is slightly higher than in thick coat and the recognition
rate in thick coat is slightly higher than in backpack. Here, after all, whether in thick coat or
in backpack, more or less, the sheltering affects the detecting accuracy to a certain extent.
When the walker is in backpack, not only sheltering but also the disturbance of additions on
body affects the accuracy. So in this situation, the recognition rates are the smallest comparing
with other walking conditions. Of course, from the whole effect, the results of the recognition
framework proposed by this paper are satisfied, and this method overcomes the limitations
Mathematical Problems in Engineering
27
Mahalanobis distance
1
1
0.9
0.9
0.8
0.8
Backpack versus thin coat
Backpack versus thin coat
Euclidean distance
0.7
0.6
0.5
0.4
0.3
0.2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0
1
Thick 0.5
0
coa
backp t versus
ack
0
1
Thick 0.5
0
coa
backp t versus
ack
0.8
0.4 0.6
at
0 0.2
ick co
h
t
ersus
v
in
h
T
0
Thin
1
0.5
k coat
ic
h
t
s
versu
a
Mahalanobis distance
Euclidean distance
0.25
1
Backpack versus thin coat
Backpack versus thin coat
0.9
0.2
0.15
0.1
0.05
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.8 0.6
0.4 0.2
Thick
coa
backp t versus
ack
0
0
1
Thick 0.5
0
coa
backp t versus
ack
0.6 0.8
t
0 0.2 0.4 s thick coa
ersu
Thin v
b
Mahalanobis distance
0.18
1
0.16
0.9
0.14
0.8
Backpack versus thin coat
Backpack versus thin coat
Euclidean distance
0.12
0.1
0.08
0.06
0.04
0.02
0
0.4 0.3
0.2 0.1
0
Thick
coat v
ersus
backp
ack
1
0.5
coat
k
0
ic
h
t
ersus
Thin v
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.4
0.2
at
0
ick co
h
t
s
u
s
r
e
v
Thin
c
0
1
0.5
0
Thick
coat v
ersus
backp
ack
Figure 20: Continued.
1
0.5
at
ick co
0
h
t
s
u
s
r
e
v
Thin
28
Mathematical Problems in Engineering
Mahalanobis distance
1
0.14
0.9
Backpack versus thin coat
Backpack versus thin coat
Euclidean distance
0.16
0.12
0.1
0.08
0.06
0.04
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.02
0.1
0
0.4
Thick 0.2
0
coa
backp t versus
ack
0
1
Thick 0.5
0
coa
backp t versus
ack
0.2
0.1 0.15
at
0 0.05 sus thick co
er
Thin v
1
0.5
at
ick co
h
0
t
s
u
s
r
e
v
in
Th
d
Mahalanobis distance
1
0.18
0.9
0.16
0.8
Backpack versus thin coat
Backpack versus thin coat
Euclidean distance
0.2
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.2
0.1
Thick
0
coat v
ersus
backp
ack
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.2
0.1 0.15
t
0 0.05 us thick coa
ers
Thin v
0
1
1
0.5
Thick 0.5
k coat
0
coat v
ic
0
h
t
s
ersus
ersu
backp
ack
Thin v
e
Figure 20: Different extent of different walking conditions at some viewing angles for each of 124 subjects.
a 54◦ viewing angle; b 72◦ viewing angle; c 90◦ viewing angle; d 108◦ viewing angle. e 126◦
viewing angle.
to some extent. That is, the recognition framework, as the gait imitation framework above, is
robust to subject’s coat or backpack to a certain extent.
Not depicting gait information in 3D, baseline method mainly studies silhouettes gait
sequences in 2D, which makes this kind of gait information’s volume and accuracy more
limited than the framework of this paper. So, its identification rates are lower than this
paper’s framework universally. In addition, at same walking conditions, its identification
rate at about 90 degree viewing angle is slightly lower than at other angles because the gait
information on frontal in silhouettes at this angle is less than at other angles, which improves
the possibility of identical detecting results among the testing samples. At the same viewing
54◦
72◦
90◦
108◦
126◦
Viewing
angle
Thin coat Thick coat Backpack
89.2
86.1
82.3
91.3
85.5
80.5
92.1
88.2
82.4
92.8
89.2
82.7
87.7
85.4
81.8
HCRF w 0 SVM
Types
HCRF w 1 SVM
HCRF w 2 SVM
Recognized rate %
Thin coat Thick coat Backpack Thin coat Thick coat Backpack
91.4
87.3
84.8
87.0
83.4
80.9
92.4
88.2
83.6
88.1
85.3
79.0
94.5
92.0
85.2
90.1
86.6
81.2
95.8
93.1
88.3
89.3
85.2
81.5
89.7
86.4
84.5
85.2
82.8
80.7
Thin coat Thick coat Backpack
81.6
75.1
68.5
80.2
74.4
67.7
78.5
72.9
65.4
79.3
73.9
68.1
82.6
76.5
69.2
Baseline method
Table 3: Associated comparisons of the integrated HCRF/SVM classifiers based on recognition application of gait imitation at different window size w and
different viewing angle with baseline method.
Mathematical Problems in Engineering
29
30
Mathematical Problems in Engineering
100
Recognition rate (%)
90
80
70
60
50
40
56
72
90
108
126
Angle of view (deg.)
HCRF + SVM; w = 0; thin coat
HCRF + SVM; w = 0; thick coat
HCRF + SVM; w = 0; backpack
HCRF + SVM; w = 1; thin coat
HCRF + SVM; w = 1; thick coat
HCRF + SVM; w = 1; backpack
HCRF + SVM; w = 2; thin coat
HCRF + SVM; w = 2; thick coat
HCRF + SVM; w = 2; backpack
Baseline method; thin coat
Baseline method; thick coat
Baseline method; backpack
Figure 21: Associated comparisons of the integrated HCRF/SVM classifiers based on recognition
application of gait imitation at different viewing angle and different window parameter w with baseline
method.
angles, the identification rate in thin coat is higher than in thick coat, and the rate in thick
coat is higher than in backpack, whose associated reasons are also the disturbances of relative
sheltering and additions on body.
Table 4 presents associated comparisons of the sole SVM or HCRF classifier on gait recognition at same window size w and different viewing angles. Figure 22 gives the bar graph
associated with data in Table 4 and data of the integrated HCRF/SVM classifier at same window size w in Table 3.
In Figure 22, at each tested visual angel, the recognition rate of HCRF SVM is
comparatively higher than HCRF or SVM solely. According to the analysis in Section 4, when
the method of NPE reduces the dimension of the time-sequences, the local neighborhood
structure on the data manifold is preserved; when the HCRF trains or infers the signs of
the time-sequences, the sequences where the underlying graphical model captures temporal
dependencies across frames is modeled and incorporates long range dependencies and when
the SVM trains or infers the final identification of the relative signs, the separating margins
of decision boundaries on classification are maximized as the data is mapped into highdimensional space. Thus, comparing with the HCRF or SVM solely, the HCRF SVM contains
more structural traits of the data to be classified during dealing with the data, which make
the recognition more sufficiently. At the phase of just after acquiring normalized parameters
of real detected object, the recognition rate of SVM is a little higher than HCRF because these
detected parameters at the same time instant are not correlated sequence in time or space,
so merits of HCRF could not be presented fully. Namely, taking the independent parameters
as correlated sequences to do with is unreasonable to some extent. And SVM is more fitting
for classifying multi-dimensional data at the same time instant than HCRF. Contrarily, at
the phase of just after reducing dimensionality of associated time-sequences, using similar
54◦
72◦
90◦
108◦
126◦
Viewing
angle
Types
Just after acquiring normalized parameters of real detected object
Just after reducing dimensionality of associated time sequences
HCRF1 w 1
SVM1
HCRF2 w 1
SVM2
Recognized rate %
Thin coat Thick coat Backpack Thin coat thick coat Backpack Thin coat Thick coat Backpack Thin coat Thick coat Backpack
63.0
58.2
55.7
69.3
64.5
60.9
73.2
70.3
61.2
69.3
67.1
55.2
64.2
60.5
54.8
72.1
65.5
55.4
75.4
70.5
62.4
72.2
65.3
58.1
66.1
61.3
56.7
75.3
67.8
58.5
78.3
72.5
65.5
75.1
66.2
58.6
73.4
67.5
55.5
74.9
69.0
58.9
80.8
78.1
66.8
78.0
66.3
59.9
65.5
61.6
57.2
68.4
64.2
56.5
74.4
71.9
64.3
70.2
63.0
56.4
Table 4: Associated comparisons of the sole SVM or HCRF classifier on gait recognition at same window size w and different viewing angles.
Mathematical Problems in Engineering
31
32
Mathematical Problems in Engineering
Recognition rate (%)
100
80
60
40
20
0
54
72
90
Angle of view (deg.)
108
126
HCRF + SVM; thin coat
HCRF + SVM; thick coat
HCRF + SVM; backpack
HCRF1; thin coat
HCRF1; thick coat
HCRF1; backpack
SVM1; thin coat
SVM1; thick coat
SVM1; backpack
HCRF2; thin coat
HCRF2; thick coat
HCRF2; backpack
SVM2; thin coat
SVM2; thick coat
SVM2; backpack
Figure 22: Associated comparisons of different classifiers in recognition application based on gait imitation
at same window size w and different viewing angles.
analysis above, the recognition rate of HCRF is a little higher than SVM of course. In addition,
for whether the sole HCRF or the sole SVM, the trends of recognition rates with viewing angle
changing is consistent with the integrated HCRF/SVM classifier above.
6. Conclusion
This paper mainly proposes a framework of human gait imitation, analogous with human
cognitive process, which integrates individual gait characteristics in reality with general
prior knowledge of human motion to realize the reconstruction of human gait in 3D from
monocular video of an uncalibrated camera directly and automatically. According to the
results of the experiment with the CASIA gait database and relative measurement, analysis,
the method in this paper is reasonable and robust to object’s clothes and backpack to a certain
extent.
In the application of this framework, firstly, all the imitated motion curves are
transformed into time-sequences with limited lengths by the means of extracting one gait
cycle, arraying in lines, reducing dimensionality with the method of NPE, in turn. Then, a
kind of classifier which integrates HCRF with SVM is used to classify the multisequences
by marking time-sequences with relative labels and classifying the labels in turn, realizing
identification recognition on human gait. At associated experiment, this kind of integrated
classification displays better properties than using HCRF or SVM solely and the typical
baselined method because it contains more structural traits of the data to be classified in
space and time during dealing with the data.
We do not think that the adopted integrated classification in this paper is the only one
and the best one suited to this human gait imitation proposed in this paper. It is just one way
and maybe there are other good classifying methods fitting for recognizing the gait imitation,
too. We do not also think that the adopted integrated classification can only deal with this
kind of dataset in this paper. Maybe it is also suitable for other kinds of datasets. Of course,
that needs new testing in other situations.
Mathematical Problems in Engineering
33
In the next work, we will investigate the imitated walking curves deeply in other
different speeds or different moods for persons and search the relative constant properties
among these curves for identification recognition. In fact, the recognition process of this paper
is two-stage of classifying process. This produces the possibility that the error aroused from
former classifier affects the last classifier, forming accumulated error. And the training time
and testing time is about 2-3 hours and 30 seconds or so, respectively. So, we will study
the two kinds of classifier more deeply in theory and manage to search only one stage of
classifying process which equals the two stages of classifying process above in theory, thus
uniting the two classifiers into one classifier is essentially to improve the accuracy and speed
of recognition.
Acknowledgments
The authors wish to thank to the National Laboratory of Pattern Recognition, Institute of
Automation of Chinese Academy of Sciences for supplying investigators who study gait with
free-CAISIA gait database. This brings us much convenience in the relative experiment of this
paper.
References
1 D. M. Gavrila and L. S. Davis, “3-D model-based tracking of humans in action: a multi-view
approach,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern
Recognition (CVPR ’96), pp. 73–80, June 1996.
2 C. Bregler and J. Malik, “Tracking people with twists and exponential maps,” in Proceedings of the
IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 8–15, Santa Barbara,
CA , USA, June 1998.
3 N. D’Apuzzo, R. Plänkers, P. Fua, A. Gruen, and D. Thalmann, “Modeling human bodies from video
sequences,” in Proceedings of the SPIE’s Electronic Imaging, vol. 3641, pp. 36–47, San Jose, Calif, USA,
January 1999.
4 J. Deutscher, A. Blake, and I. Reid, “Articulated body motion capture by annealed particle filtering,”
in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 126–133, June 2000.
5 J. Darby, B. Li, and N. Costen, “Tracking human pose with multiple activity models,” Pattern
Recognition, vol. 43, no. 9, pp. 3042–3058, 2010.
6 N. R. Howe, M. E. Leventon, and W. T. Freeman, “Bayesian reconstruction of 3d human motion from
single-camera video,” in Proceedings of the Advances in Neural Information Processing Systems, pp. 820–
826, 1999.
7 H. Ning, T. Tan, L. Wang, and W. Hu, “Kinematics-based tracking of human walking in monocular
video sequences,” Image and Vision Computing, vol. 22, no. 5, pp. 429–441, 2004.
8 Z. Ziheng, A. Prügel-Bennett, and R. I. Damper, “A bayesian framework for extracting human gait
using strong prior knowledge,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28,
no. 11, pp. 1738–1752, 2006.
9 W. Wang, X. Deng, X. Qiu, S. Xia, and Z. Wang, “Learning local models for 2D human motion
tracking,” in Proceedings of the IEEE International Conference on Image Processing (ICIP ’09), pp. 2589–
2592, November 2009.
10 F. Remondino and A. Roditakis, “Human figure reconstruction and modeling from single image or
monocular video sequence,” in Proceedings of the Fourth International Conference on 3-D Digital Imaging
and Modeling (3DIM ’03), 2003.
11 U. Gaur, A. Jain, and S. Goel, “Towards real-time monocular video-based avatar animation,” Lecture
Notes in Computer Science, vol. 5359, no. 2, pp. 949–958, 2008.
12 B. Zou, S. Chen, C. Shi, and U. M. Providence, “Automatic reconstruction of 3D human motion pose
from uncalibrated monocular video sequences based on markerless human motion tracking,” Pattern
Recognition, vol. 42, no. 7, pp. 1559–1571, 2009.
34
Mathematical Problems in Engineering
13 C. Sminchisescu and B. Triggs, “Covariance scaled sampling for monocular 3D body tracking,” in
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. I447–
I454, December 2001.
14 A. D. Sappa, N. Aifanti, S. Malassiotis, and M. G. Strintzis, “3D gait estimation from monoscopic
video,” in Proceedings of the International Conference on Image Processing (ICIP ’04), pp. 1963–1966,
October 2004.
15 R. D. Green and L. Guan, “Quantifying and recognizing human movement patterns from monocular
video images—part I: a new framework for modeling human motion,” IEEE Transactions on Circuits
and Systems for Video Technology, vol. 14, no. 2, pp. 179–190, 2004.
16 R. D. Green and L. Guan, “Quantifying and recognizing human movement patterns from monocular
video images—part II applications to biometrics,” IEEE Transactions on Circuits and Systems for Video
Technology, vol. 14, no. 2, pp. 191–198, 2004.
17 X. Zhao and Y. Liu, “Generative tracking of 3D human motion by hierarchical annealed genetic
algorithm,” Pattern Recognition, vol. 41, no. 8, pp. 2470–2483, 2008.
18 R. M. Gray, Entropy and Information Theory, Springer, New York, NY, USA, 1990.
19 F. Escolano, P. Suau, and B. Bonev, Information Theory in Computer Vision and Pattern Recognition, 2009.
20 H-ANIM WEB SITE, http://www.h-anim.org/.
21 VRML WEB SITE, http://www.vrmlsite.com/.
22 D. A. Winter, Biomechanics and Motor Control of Human Movement, Wiley-Interscience, 2nd edition,
1990.
23 J. H. Yoo, M. S. Nixon, and C. J. Harris, “Extracting human gait signatures by body segment properties,” in Proceedings of the 5th IEEE Southwest Symposium on Image Analysis and Interpretation, 2002.
24 W. T. Dempster and G. R. L. Gaughran, “Properties of body segments based on size and weight,”
American Journal of Anatomy, vol. 120, no. 1, pp. 33–54, 1967.
25 R. Boulic, N. M. Thalmann, and D. Thalmann, “A global human walking model with real-time
kinematic personification,” The Visual Computer, vol. 6, no. 6, pp. 344–358, 1990.
26 M. P. Murray, “Gait as a total pattern of movement,” American Journal of Physical Medicine, vol. 46, no.
1, pp. 290–333, 1967.
27 M. Murray, A. B. Drought, and R. C. Kory, “Walking patterns of normal men,” The Journal of Bone and
Joint Surgery, vol. 46, pp. 335–360, 1964.
28 M. P. Murray, R. C. Kory, B. H. Clarkson, and S. B. Sepic, “Comparison of free and fast speed walking
patterns of normal men,” American Journal of Physical Medicine, vol. 45, no. 1, pp. 8–23, 1966.
29 P. A. Hageman and D. J. Blanke, “Comparison of gait of young women and elderly women,” Physical
Therapy, vol. 66, no. 9, pp. 1382–1387, 1986.
30 K. M. Ostrosky, J. M. VanSwearingen, R. G. Burdett, Z. Gee, and M. Eastlack, “A comparison of gait
characteristics in young and old subjects,” Physical Therapy, vol. 74, no. 7, pp. 637–646, 1994.
31 G. Bradski and A. Kaehler, Learning OpenCV: Computer Vision with the OpenCV library, O’Reilly Media,
Inc., 2008.
32 D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to
represent a digitized line or its caricature,” Cartographica, vol. 10, no. 2, pp. 112–122, 1973.
33 X. He, D. Cai, S. Yan, and H. J. Zhang, “Neighborhood preserving embedding,” in Proceedingsof the
10th IEEE International Conference on Computer Vision (ICCV ’05), pp. 1208–1213, October 2005.
34 A. Quattoni, S. Wang, L. P. Morency, M. Collins, and T. Darrell, “Hidden conditional random fields,”
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 10, pp. 1848–1853, 2007.
35 S. Abe, Support Vector Machines for Pattern Classification, Springer, London, UK, 2nd edition, 2010.
36 S. B. Wang, A. Quattoni, L. P. Morency, D. Demirdjian, and T. Darrell, “Hidden conditional random
fields for gesture recognition,” in Proceedings of the IEEE Computer Society Conference on Computer Vision
and Pattern Recognition (CVPR ’06), pp. 1521–1527, June 2006.
37 L. P. Morency, A. Quattoni, C. M. Christoudias, and S. Wang, Hidden-state Conditional Random Field
Library. User Guide, 2008.
38 W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an
efficient line search,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 170–192, 2005.
39 C. W. Hsu and C. J. Lin, “A comparison of methods for multiclass support vector machines,” IEEE
Transactions on Neural Networks, vol. 13, no. 2, pp. 415–425, 2002.
40 J. Friedman, “Another approach to polychotomous classification,” Tech. Rep., Department of
Statistics, Stanford University, 1996.
Mathematical Problems in Engineering
35
41 O. Chapelle, P. Haffner, and V. N. Vapnik, “Support vector machines for histogram-based image
classification,” IEEE Transactions on Neural Networks, vol. 10, no. 5, pp. 1055–1064, 1999.
42 C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” Science, vol. 2, no. 3, pp.
1–39, 2001.
43 S. Yu, D. Tan, and T. Tan, “A framework for evaluating the effect of view angle, clothing and carrying
condition on gait recognition,” in Proceedings of the 18th International Conference on Pattern Recognition
(ICPR ’06), pp. 441–444, August 2006.
44 S. Sarkar, P. J. Phillips, Z. Liu, I. R. Vega, P. Grother, and K. W. Bowyer, “The humanID gait challenge
problem: data sets, performance, and analysis,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 27, no. 2, pp. 162–177, 2005.
Advances in
Operations Research
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Advances in
Decision Sciences
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Mathematical Problems
in Engineering
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Journal of
Algebra
Hindawi Publishing Corporation
http://www.hindawi.com
Probability and Statistics
Volume 2014
The Scientific
World Journal
Hindawi Publishing Corporation
http://www.hindawi.com
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
International Journal of
Differential Equations
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Volume 2014
Submit your manuscripts at
http://www.hindawi.com
International Journal of
Advances in
Combinatorics
Hindawi Publishing Corporation
http://www.hindawi.com
Mathematical Physics
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Journal of
Complex Analysis
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
International
Journal of
Mathematics and
Mathematical
Sciences
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com
Stochastic Analysis
Abstract and
Applied Analysis
Hindawi Publishing Corporation
http://www.hindawi.com
Hindawi Publishing Corporation
http://www.hindawi.com
International Journal of
Mathematics
Volume 2014
Volume 2014
Discrete Dynamics in
Nature and Society
Volume 2014
Volume 2014
Journal of
Journal of
Discrete Mathematics
Journal of
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Applied Mathematics
Journal of
Function Spaces
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Optimization
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014